Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
360 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 117 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q16×D131 | C2 | semidirect |
| 3. #22553751 | C2 | direct (N × H) |
| 4. C2×Dic1048 | C2 | semidirect |
| 5. C2×#16862192 | C2 | semidirect |
| 6. C2×#16862190 | C2 | semidirect |
| 7. C2×#16862185 | C2 | semidirect |
| 8. C2×SD32×C131 | C2 | semidirect |
| 17. Q16×D131 | C22 | semidirect |
| 20. Dic1048 | C22 | semidirect |
| 21. #16862192 | C22 | semidirect |
| 22. #16862190 | C22 | semidirect |
| 23. #16862185 | C22 | semidirect |
| 27. SD32×C131 | C22 | semidirect |
| 94. C2×C131 | #510 | semidirect |
| 97. C131 | C2×#510 | semidirect |
| 105. C2×SD32 | D131 | semidirect |
| 123. SD32 | C2×D131 | semidirect |
| 193. C2 | #22553751 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862265 | 2 |
| C2×Q16×D131 | 2 |
| #22553751 | 2 |
| C2×Dic1048 | 2 |
| C2×#16862192 | 2 |
| C2×#16862190 | 2 |
| C2×#16862185 | 2 |
| C2×SD32×C131 | 2 |
| C2×#510 | 131 |